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An inlet tap can fill water at the rate of 20 litres per minute. Now, before opening the inlet tap they found a leak in the tank which can empty the tank in 8 hours. They could not repair the leak and opened the inlet tap when the tank was full and it empties the tank in 10 hours. Find the capacity of tank.

An inlet tap can fill water at the rate of 20 litres per minute. Now, before opening the inlet tap they found a leak in the tank which can empty the tank in 8 hours. They could not repair the leak and opened the inlet tap when the tank was full and it empties the tank in 10 hours. Find the capacity of tank. Correct Answer 48000 litres

Given:

Flow of inlet tap per minute = 20 litres

Leak can empty the tank in 8 hours

If the inlet tap is opened and leak is also there then it empties the tank in 10 hours

Concept used:

Work = Time taken × efficiency

And, efficiency of emptying taps is taken in negative

Calculation used:

Let the total work be x

Leak can empty the tank in 8 hours

Efficiency of leak = -x/8

Leak with inlet tap can empty the tank in 10 hours

Efficiency of leak with inlet tap = -x/10

Now efficiency of inlet tap = -x/10 – (-x/8) = -x/10 + x/8

⇒ Efficiency of inlet tap = x/40

Now the time taken by inlet tap = (x ÷ x/40)

⇒ Time taken by inlet tap = 40 hours = 2400 minutes

Total capacity of tank = (2400 × 20) litres

⇒ Total capacity of tank = 48000 litres

∴ The capacity of the tank is 48000 litres

 Confusion Points Flow of inlet tap per minute = 20 litres

We have multiplied by 60 to make Flow of inlet tap per hour.

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